If the outdoor fan isn't running but you can hear a hum, it's most likely the capacitor. Google A/C capacitors to get a good idea of what they look like. If you can operate a screw driver, you've got the ability to replace a capacitor. The size of the capacitor should be indicated on it, and you can easily order a new one online. Just be careful. Capacitor's are designed to hold a charge and can deliver quite a shock.
If it's not running and there's no noise, check the breakers and/or fuses. There should be a breaker for the unit in your indoor breaker box, and there should be a disconnect box (where you can cut power to the unit) outside at the unit. Some of these disconnect boxes have fuses inside.
If everything's running, it's probably a refrigerant issue. Most people aren't going to have the tools for that and you'll just have to call somebody. If it is a refrigerant issue, you've got a leak that needs to be found and sealed.